Question 1

Definition check: In network theorems, the Norton equivalent current corresponds to which quantity at the output terminals?

Accepted Answer

Introduction / Context: The Norton and Thevenin equivalents simplify complex linear circuits. Correctly identifying the Norton current is essential for quick hand analysis and for converting between Norton and Thevenin forms. Given Data / Assumptions: Linear bilateral network assumptions apply. We are concerned with the equivalent seen at two output terminals. Independent sources are active; dependent sources are treated per standard procedures. Concept / Approach: The Norton form is a current source IN in parallel with an equivalent resistance RN. The defining current IN is by definition the short-circuit current at the output terminals (i_sc). RN equals the Thevenin resistance RTH, found by deactivating independent sources or via test sources when dependent sources exist. Step-by-Step Solution: To find IN, short the output terminals.Compute the resulting current from the network into the short: IN = i_sc.Keep RN = RTH to complete the Norton pair. Verification / Alternative check: Conversion check: The Thevenin equivalent voltage VTH equals IN * RN. Measuring either i_sc or VTH with RN provides mutual confirmation of the equivalence. Why Other Options Are Wrong: 'The current through the load' depends on load value and is not an invariant equivalent parameter. 'Open-current from the source' is undefined; open-circuit relates to Thevenin voltage, not Norton current. 'None of the above' is incorrect because a standard definition exists. Common Pitfalls: Confusing i_sc (Norton current) with I_load at arbitrary loads; forgetting that RTH = RN during conversions. Final Answer: the short circuit current

Question 2

In AC circuit analysis using Thevenin’s theorem, the reduced Thevenin equivalent seen by a load consists of which two components? Select the most accurate pair for sinusoidal steady-state (phasor) conditions.

Accepted Answer

Introduction / Context: Thevenin’s theorem is a cornerstone of network reduction in electrical engineering. For any linear, bilateral network seen from two terminals, we can compute an equivalent that behaves identically at those terminals. In alternating current (AC) phasor analysis, this equivalent is expressed with complex quantities to capture both resistance and reactance, allowing us to predict current, voltage, and power for any attached load quickly. Given Data / Assumptions: We are working under sinusoidal steady-state, so impedances (not just resistances) represent elements. The original network is linear and bilateral. We want the correct composition of the Thevenin equivalent as seen by a load. Concept / Approach: The Thevenin equivalent across two terminals is formed by: (1) the open-circuit (no-load) voltage at those terminals, called V_TH, and (2) an equivalent series impedance Z_TH that accounts for the network’s internal opposition to current (including resistive and reactive parts). Z_TH is found by deactivating independent sources (voltage sources shorted, current sources opened) and calculating the equivalent impedance seen into the network. Step-by-Step Solution: Identify Thevenin voltage: V_TH = V_OC (phasor open-circuit terminal voltage).Identify Thevenin impedance: Z_TH = equivalent series impedance seen at the terminals with independent sources deactivated.Therefore, the Thevenin equivalent is a single ideal voltage source V_TH in series with Z_TH. Verification / Alternative check: Replace the reduced model with an arbitrary load Z_L. Compute I = V_TH / (Z_TH + Z_L). If you instead analyze the original network directly, you obtain the same terminal current and load voltage. This identity validates that the pair {V_TH, Z_TH in series} completely characterizes terminal behavior. Why Other Options Are Wrong: 'the equivalent voltage source and the equivalent series resistance': In AC phasor form, opposition is complex; using only resistance ignores reactance, so this is incomplete. 'the equivalent voltage source and the equivalent parallel impedance': Thevenin uses a series element; a parallel form corresponds to Norton after source conversion. 'the equivalent voltage source and the equivalent parallel resistance': Again, parallel form is a Norton construct and resistance alone is insufficient in AC. Common Pitfalls: Confusing Thevenin (series source + series impedance) with Norton (current source + parallel admittance/impedance) forms. Forgetting to deactivate sources correctly when computing Z_TH (short ideal voltage sources, open ideal current sources). Final Answer: the equivalent voltage source and the equivalent series impedance

Question 3

According to the superposition theorem for linear circuits in phasor (AC) analysis, how should multiple independent sources be handled when determining currents or voltages at a given element?

Accepted Answer

Introduction / Context: The superposition theorem enables stepwise analysis of linear circuits containing multiple independent sources. It is especially useful in AC phasor analysis where each source may have distinct magnitude and phase. By evaluating one source at a time while properly deactivating the others, we can sum the resulting phasor contributions to find the total response. Given Data / Assumptions: The circuit is linear and time-invariant. We are performing AC phasor analysis (complex impedances). Multiple independent sources (voltage and/or current) exist. Concept / Approach: Superposition states that the total response equals the sum of individual responses due to each independent source acting alone. When considering one source, all other independent voltage sources are replaced by their internal impedance (ideal voltage source → short circuit; finite source resistance/impedance remains). Independent current sources are opened (ideal current source → open circuit; any internal impedance remains). Dependent sources, if present, are not deactivated because they depend on circuit variables. Step-by-Step Solution: Select one independent source; deactivate the others by replacing them with their internal impedances.Solve the circuit (using KVL/KCL, Ohm’s law, or impedance combinations) to find the partial response.Repeat for each source and sum all phasor results algebraically to get the total voltage/current. Verification / Alternative check: As a check, you can analyze the full circuit with all sources active at once (e.g., by nodal analysis). The resulting voltages and currents will match the phasor sum obtained via superposition if the circuit is linear. Why Other Options Are Wrong: 'all sources are considered independently': Too vague; the method requires specific deactivation rules using internal impedance. 'all sources are considered simultaneously': That is a valid direct solve, but not the definition of superposition. 'internal resistance': In AC phasor analysis, elements contribute complex impedance; limiting to resistance omits reactance and is incorrect. Common Pitfalls: Deactivating dependent sources (should remain active). Forgetting that ideal voltage source → short, ideal current source → open. Final Answer: the sources are considered one at a time with all others replaced by their internal impedance

Question 4

Definition check: In Thevenin’s theorem, the Thevenin equivalent voltage seen at two terminals equals which measurable quantity of the original network?

Accepted Answer

Introduction / Context: Thevenin’s theorem allows any linear two-terminal network to be represented by a single ideal voltage source in series with an equivalent impedance. Correctly identifying the Thevenin voltage, V_TH, is essential to build this model and to predict how different loads will behave when connected across the terminals. Given Data / Assumptions: We are analyzing a linear, bilateral circuit in steady state. No load is connected while determining V_TH. Measurements are made at the two terminals of interest. Concept / Approach: The Thevenin equivalent voltage, V_TH, is by definition the terminal voltage with the load removed, i.e., the open-circuit voltage V_OC. With no load, there is no current through the external terminals; internal source and network interactions fix the terminal potential, which becomes V_TH. Once V_TH is known and Z_TH computed, any load response follows from simple voltage division in the Thevenin model. Step-by-Step Solution: Remove the load to create an open circuit at the terminals.Compute or measure the terminal voltage under open-circuit conditions: V_OC.Assign V_TH = V_OC (phasor in AC analysis). Verification / Alternative check: Connect a test load Z_L and predict the load voltage using the Thevenin model: V_L = V_TH * Z_L / (Z_TH + Z_L). If you instead compute V_L directly on the original network, results will match, confirming that V_TH was correctly identified as V_OC. Why Other Options Are Wrong: 'equal to the source voltage': Internal drops may make the terminal voltage differ from the source value; only in trivial cases are they equal. 'the same as the load voltage': Load voltage depends on Z_L and is not defined for the open-circuit condition. 'none of the above': Incorrect because V_TH explicitly equals the open-circuit terminal voltage. Common Pitfalls: Confusing V_TH with the internal source value instead of the measurable terminal voltage without load. Attempting to find V_TH with the load still connected. Final Answer: the open circuit voltage

Question 5

According to network theorems in electrical engineering, Norton's theorem replaces any linear two-terminal network by which form of equivalent source-and-impedance model?

Accepted Answer

Introduction / Context: Norton's theorem is a cornerstone of circuit simplification in electrical engineering. It allows you to replace any linear, bilateral two-terminal network (containing independent/dependent sources and resistances/impedances) with an equivalent model that is easier to analyze—especially for varying loads and parallel interconnections. Given Data / Assumptions: The original network is linear and time-invariant. All frequency-domain impedances are allowed (R, L, C) as a single equivalent impedance. The theorem is applied at a specific pair of output terminals. Concept / Approach: Norton's theorem states that a two-port seen from its output terminals is equivalent to a current source IN in parallel with an impedance RN (also written ZN). IN is the short-circuit current at the terminals, and RN equals the Thevenin resistance RTH (found by deactivating independent sources, or by test-source methods when dependent sources are present). Step-by-Step Solution: Identify the two terminals where the load connects; remove the load.Find IN: short the terminals and compute the resulting current (short-circuit current).Find RN: deactivate independent sources (voltage sources → short, current sources → open) and compute the equivalent resistance seen into the network; or apply a test source if dependent sources exist.Form the Norton equivalent as IN in parallel with RN. Verification / Alternative check: Convert between Thevenin and Norton to verify: VTH = IN * RN and RTH = RN. Analyzed with any load RL, the Norton and Thevenin forms yield identical terminal currents and voltages. Why Other Options Are Wrong: 'Voltage source in series with impedance' is Thevenin, not Norton. 'Current source in series with impedance' is not a standard canonical form. 'Voltage source in parallel with impedance' also does not match Norton's canonical form. Common Pitfalls: Confusing IN with load current (IN is the short-circuit current), and forgetting that RN equals RTH. Also, failing to treat dependent sources correctly when computing RN. Final Answer: an equivalent current source in parallel with an equivalent impedance

Question 6

Instantaneous direction matters: If two time-varying currents flow in the same direction through a single branch at an instant, what is the instantaneous net branch current?

Accepted Answer

Introduction / Context: Superposition and current addition are foundational concepts in circuit theory. In practical signal paths, multiple sources (or coupled subcircuits) can drive current through the same branch. Understanding how instantaneous currents combine ensures correct sizing of components and accurate waveform analysis. Given Data / Assumptions: Two currents, i1(t) and i2(t), exist in the same branch at the same instant. Their directions at that instant are the same (defined by the same reference direction). Linear network behavior is assumed for superposition reasoning, but instantaneous algebra applies generally. Concept / Approach: Currents are signed quantities. When two currents share the same direction at an instant, their instantaneous values add arithmetically. The net branch current equals i_net(t) = i1(t) + i2(t). If one were opposite in direction, it would subtract based on the chosen sign convention. Step-by-Step Solution: Choose a reference direction for the branch current (e.g., left to right).At a given time t0, measure i1(t0) and i2(t0). Both are positive in the reference direction.Compute instantaneous net: i_net(t0) = i1(t0) + i2(t0).Resulting net waveform is the pointwise sum over time: i_net(t) = i1(t) + i2(t). Verification / Alternative check: Kirchhoff's Current Law (KCL) at any node confirms current conservation. In a series branch, currents must be equal through elements; when multiple source contributions are present, they superimpose linearly with signs set by direction. Why Other Options Are Wrong: 'Difference' applies only when currents are in opposite directions under the chosen sign. 'Zero' would require equal magnitudes but opposite directions. 'Cannot be determined' is incorrect because direction and magnitudes at the instant uniquely define the sum. Common Pitfalls: Mixing phasor addition with instantaneous addition; forgetting to apply consistent sign conventions; assuming RMS values can be simply added without considering phase. Final Answer: is the sum of the two currents

Question 7

Maximum power transfer from a capacitive source: What must the load impedance be relative to the source impedance to achieve maximum power transfer?

Accepted Answer

Introduction / Context: The maximum power transfer (MPT) condition is crucial in communications, RF design, and audio interfaces. When reactive elements are present, merely matching magnitudes is insufficient; the phase (reactive sign) must be addressed to ensure full power delivery from source to load. Given Data / Assumptions: Source represented by Thevenin or Norton equivalent with complex impedance Zs = Rs + jXs. Load impedance ZL is selectable. Sinusoidal steady-state operation in the frequency domain. Concept / Approach: For AC circuits with reactance, the MPT condition is ZL = Zs* (complex conjugate). This means RL = Rs (equal resistive parts) and XL = −Xs (reactive parts cancel). For a capacitive source (Xs < 0), the load must be inductive with equal magnitude reactance (XL > 0) to neutralize the reactive component at the interface. Step-by-Step Solution: Let Zs = Rs − j|Xs| (capacitive).Choose ZL = Rs + j|Xs| (inductive) so ZL = Zs*.The combined transfer at the operating frequency sees purely resistive interaction, maximizing power delivered to RL.Result: Maximum average power occurs when ZL = Zs*. Verification / Alternative check: Differentiate the real power delivered to the load with respect to RL and XL; the optimum occurs at RL = Rs and XL = −Xs. RF matching networks implement this with L- or pi-networks that create the conjugate at the design frequency. Why Other Options Are Wrong: 'Capacitive reactance equal to circuit resistance' mixes units and ignores the reactive sign. 'Be as capacitive as it is inductive' is meaningless without phase relation. 'None of the above' is false because a well-defined condition exists: conjugate matching. Common Pitfalls: Confusing DC (where XL = 0) with AC matching; attempting magnitude-only matching; forgetting that MPT can increase losses in some systems where efficiency, not power, is prioritized. Final Answer: have an impedance that is the complex conjugate of the source impedance

Question 8

Thevenin's theorem provides a method for the reduction of any ac circuit to an equivalent form consisting of an equivalent current source in parallel with an equivalent impedance.

Accepted Answer

False

Question 9

The superposition theorem is useful for the analysis of single-source circuits.

Accepted Answer

False

Question 10

An equivalent circuit is one that produces the same voltage and current to a given load as the original circuit that it replaces.

Accepted Answer

True

Question 11

In order to get maximum power transfer from a capacitive source, the load must have an impedance that is the complex conjugate of the source impedance.

Accepted Answer

True

Question 12

One circuit is equivalent to another, in the context of Thevenin's theorem, when the circuits produce the same voltage.

Accepted Answer

False

Question 13

A Thevenin ac equivalent circuit always consists of an equivalent ac voltage source and an equivalent capacitance.

Accepted Answer

False

Question 14

The superposition theorem is useful for circuit analysis only in ac circuits.

Accepted Answer

False

Question 15

Like Thevenin's theorem, Norton's theorem provides a method of reducing a more complex circuit to a simpler, more manageable form for analysis.

Accepted Answer

True

Question 16

Norton's theorem provides a method for the reduction of any ac circuit to an equivalent form consisting of an equivalent voltage source in series with an equivalent impedance.

Accepted Answer

False

Question 17

In an ac circuit, power to the load peaks at the frequency at which the load impedance is the complex conjugate of the output impedance.

Accepted Answer

True

Circuit Theorems in AC Analysis Questions